WORST_CASE(?,O(n^1)) * Step 1: Ara WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: goal(xs) -> ordered(xs) notEmpty(Cons(x,xs)) -> True() notEmpty(Nil()) -> False() ordered(Cons(x,Nil())) -> True() ordered(Cons(x',Cons(x,xs))) -> ordered[Ite](<(x',x),Cons(x',Cons(x,xs))) ordered(Nil()) -> True() - Weak TRS: <(x,0()) -> False() <(0(),S(y)) -> True() <(S(x),S(y)) -> <(x,y) ordered[Ite](False(),xs) -> False() ordered[Ite](True(),Cons(x',Cons(x,xs))) -> ordered(xs) - Signature: { "A"(0) < :: ["A"(0) x "A"(0)] -(0)-> "A"(15) Cons :: ["A"(1) x "A"(1)] -(1)-> "A"(1) Cons :: ["A"(3) x "A"(3)] -(3)-> "A"(3) False :: [] -(0)-> "A"(7) False :: [] -(0)-> "A"(15) Nil :: [] -(0)-> "A"(1) Nil :: [] -(0)-> "A"(3) S :: ["A"(0)] -(0)-> "A"(0) True :: [] -(0)-> "A"(7) True :: [] -(0)-> "A"(15) goal :: ["A"(13)] -(12)-> "A"(2) notEmpty :: ["A"(1)] -(11)-> "A"(0) ordered :: ["A"(3)] -(10)-> "A"(12) ordered[Ite] :: ["A"(7) x "A"(3)] -(4)-> "A"(12) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "0_A" :: [] -(0)-> "A"(1) "Cons_A" :: ["A"(1) x "A"(1)] -(1)-> "A"(1) "False_A" :: [] -(0)-> "A"(1) "Nil_A" :: [] -(0)-> "A"(1) "S_A" :: ["A"(1)] -(1)-> "A"(1) "True_A" :: [] -(0)-> "A"(1) WORST_CASE(?,O(n^1))